Representing Data - GCSE Maths - Steps, Examples & Worksheet - Free Printable

It looks like you've uploaded an image containing several data representation tasks. I'll go through each section one by one and solve the problems, explaining the steps clearly.

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1. Tally Chart – Sports

We are given a tally chart with incomplete frequency values. Let's interpret it.

| Sport | Tally | Frequency |
|-----------|-------|-----------|
| Cricket | |||| ||| | 8 |
| Soccer | |||| |||| ||| | 13 |
| Tennis | |||| ||| | 8 |
| Rugby | |||| || | 7 |

Explanation:
- Each "||||" represents 4 (a group of 5), but in this case, we count individual tallies.
- In tally marks:
- Every fifth mark is diagonal across the previous four.
- So:
- Cricket: 8 marks → 8
- Soccer: 13 marks → 13
- Tennis: 8 marks → 8
- Rugby: 7 marks → 7

✔ The frequencies are already filled in correctly.

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2. Pictogram – Parcels Delivered

We have a pictogram where each circle (●) represents 4 parcels, as per the key.

| Town | Pictogram | Calculation | Total Parcels |
|------------|-----------|-------------|----------------|
| Bristol | ●●● | 3 × 4 = 12 | 12 |
| Cardiff | ●●●½ | 3.5 × 4 = 14 | 14 |
| Manchester | ●●●¼ | 3.25 × 4 = 13 | 13 |
| Reading | ●●½ | 2.5 × 4 = 10 | 10 |
| Leeds | ●●●½ | 3.5 × 4 = 14 | 14 |

Explanation:
- Each full circle = 4 parcels
- Half circle = 2 parcels
- Quarter circle = 1 parcel

So:
- Bristol: 3 circles → 3 × 4 = 12
- Cardiff: 3 full + 1 half → 3×4 + 2 = 14
- Manchester: 3 full + 1 quarter → 3×4 + 1 = 13
- Reading: 2 full + 1 half → 2×4 + 2 = 10
- Leeds: 3 full + 1 half → 3×4 + 2 = 14

✔ Final totals:

| Town | Parcels |
|------------|---------|
| Bristol | 12 |
| Cardiff | 14 |
| Manchester | 13 |
| Reading | 10 |
| Leeds | 14 |

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3. Two-Way Table – Tea and Coffee Preferences

We're given a table with some missing values. Let’s fill it in using logic.

| | Male | Female | Total |
|-----------|------|--------|-------|
| Tea | 28 | 40 | 68 |
| Coffee | 50 | 20 | 70 |
| Neither | 20 | 30 | 50 |
| Total | 98 | 90 | 188 |

Let’s verify:

- Tea total: 28 (M) + 40 (F) = 68 ✔
- Coffee total: 50 + 20 = 70 ✔
- Neither total: 20 + 30 = 50 ✔
- Male total: 28 + 50 + 20 = 98 ✔
- Female total: 40 + 20 + 30 = 90 ✔
- Grand total: 98 + 90 = 188 ✔

All values are consistent.

✔ The table is complete and correct.

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4. Line Graph – Number of People (Mon–Sun)

The graph shows daily counts from Monday to Sunday.

Let’s read the values from the graph:

- Monday (M): 1
- Tuesday (T): 3
- Wednesday (W): 4
- Thursday (Th): 2
- Friday (F): 3
- Saturday (S): 5
- Sunday (Su): 3

Explanation:
- The x-axis is days of the week.
- The y-axis is number of people (from 0 to 5).
- We read the point on the graph for each day.

So the data is:

| Day | Number of People |
|-----------|------------------|
| Monday | 1 |
| Tuesday | 3 |
| Wednesday | 4 |
| Thursday | 2 |
| Friday | 3 |
| Saturday | 5 |
| Sunday | 3 |

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✔ Summary of All Solutions:

#### 1. Tally Chart
- Cricket: 8
- Soccer: 13
- Tennis: 8
- Rugby: 7

#### 2. Pictogram (Parcels)
- Bristol: 12
- Cardiff: 14
- Manchester: 13
- Reading: 10
- Leeds: 14

#### 3. Two-Way Table
- All values are correct and consistent:
- Total = 188
- Males = 98, Females = 90

#### 4. Line Graph
- Daily values: M=1, T=3, W=4, Th=2, F=3, S=5, Su=3

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